Hop Test SR Results
Mick Girdwood
03 June, 2024
Within Person
1. Single Hop - Within Person
Specify covariance matrix
Need to create a full covariance matrix. Using
clubSandwhich package to help Assuming a correlation of
0.85 between timepoints.
Model Selection
Data are now ready for meta-analysis
Need to now decide on how to fit models. Several different structures were trialed in piloting.
Based on piloting best results were achieved with fitting random effects for timepoints, nested within cohorts. Trialled fitting extra random effects e.g. effect size id (es_id), as well as separate models where study group was also a separate random effect, however resulting models were too complex, with indistinguishable random effects and overall a simpler model chosen.
Decision making here revolves around how to fit the timepoint
predictor - i.e. what sort of relationship is present between
yi and timepoint Different models are
generated then using fit statistics (AIC, BIC, AIcc), visual inspection
of fit and expected fit based on knowledge to decide on best fit.
5 different shapes of fit tried: - linear - log - polynomial - 3 knot restricted cubic spline - 4 knot restricted cubic spline
## [[1]]
## mod logLik. deviance. AIC. BIC. AICc.
## 1 Linear 222.3709 -444.7419 -436.7419 -424.5425 -436.4770
## 2 Log 234.8248 -469.6496 -461.6496 -449.4502 -461.3847
## 3 Poly (2) 225.7822 -451.5643 -441.5643 -426.3472 -441.1617
## 4 3 knot RCS 231.0868 -462.1736 -452.1736 -436.9565 -451.7709
## 5 4 knot RCS 258.3506 -516.7012 -504.7012 -486.4795 -504.1298
##
## [[2]]
Final Model - Single Leg Hop
##
## Multivariate Meta-Analysis Model (k = 158; method: REML)
##
## Variance Components:
##
## outer factor: cohort (nlvls = 114)
## inner factor: timepoint_mean (nlvls = 94)
##
## estim sqrt fixed
## tau^2 0.0023 0.0477 no
## rho 0.9715 no
##
## Test for Residual Heterogeneity:
## QE(df = 154) = 2846.1799, p-val < .0001
##
## Number of estimates: 158
## Number of clusters: 114
## Estimates per cluster: 1-5 (mean: 1.39, median: 1)
##
## Test of Moderators (coefficients 2:4):¹
## F(df1 = 3, df2 = 25.18) = 73.0069, p-val < .0001
##
## Model Results:
##
## estimate se¹ tval¹ df¹
## intrcpt -0.3318 0.0177 -18.7525 17.19
## rcs(timepoint_mean, 4)timepoint_mean 0.0316 0.0023 13.9569 17.2
## rcs(timepoint_mean, 4)timepoint_mean' -0.9673 0.0790 -12.2451 21.27
## rcs(timepoint_mean, 4)timepoint_mean'' 1.6875 0.1396 12.0888 21.77
## pval¹ ci.lb¹ ci.ub¹
## intrcpt <.0001 -0.3691 -0.2945 ***
## rcs(timepoint_mean, 4)timepoint_mean <.0001 0.0268 0.0363 ***
## rcs(timepoint_mean, 4)timepoint_mean' <.0001 -1.1314 -0.8031 ***
## rcs(timepoint_mean, 4)timepoint_mean'' <.0001 1.3978 1.9772 ***
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## 1) results based on cluster-robust inference (var-cov estimator: CR2,
## approx t/F-tests and confidence intervals, df: Satterthwaite approx)## Profiling tau2 = 1
## Profiling rho = 1
| 1 year | 2 years | 5 years | Zero crossing | Last Data Point |
|---|---|---|---|---|
| 93.8 (92.8 to 94.9) | 93.5 (92.3 to 94.7) | 94.2 (93.1 to 95.3) | NA | 106 months |
## [1] 35.80413## [1] 4.099606 8.100000 13.500000 62.4000002. Triple Hop
Specify covariance matrix
Model Selection
## [[1]]
## mod logLik. deviance. AIC. BIC. AICc.
## 1 Linear 69.59918 -139.1984 -131.1984 -123.6311 -130.2893
## 2 Log 74.63269 -149.2654 -141.2654 -133.6981 -140.3563
## 3 Poly (2) 71.37856 -142.7571 -132.7571 -123.4011 -131.3285
## 4 3 knot RCS 73.92010 -147.8402 -137.8402 -128.4842 -136.4116
## 5 4 knot RCS 73.95875 -147.9175 -135.9175 -124.8166 -133.8175
##
## [[2]]
Final Model - Triple Hop
(not crossover)
##
## Multivariate Meta-Analysis Model (k = 51; method: REML)
##
## Variance Components:
##
## outer factor: cohort (nlvls = 40)
## inner factor: timepoint_mean (nlvls = 38)
##
## estim sqrt fixed
## tau^2 0.0029 0.0536 no
## rho 0.9425 no
##
## Test for Residual Heterogeneity:
## QE(df = 49) = 828.4431, p-val < .0001
##
## Number of estimates: 51
## Number of clusters: 40
## Estimates per cluster: 1-3 (mean: 1.27, median: 1)
##
## Test of Moderators (coefficient 2):¹
## F(df1 = 1, df2 = 12.96) = 28.4696, p-val = 0.0001
##
## Model Results:
##
## estimate se¹ tval¹ df¹ pval¹ ci.lb¹
## intrcpt -0.1934 0.0267 -7.2552 20.03 <.0001 -0.2490
## log(timepoint_mean) 0.0509 0.0095 5.3357 12.96 0.0001 0.0303
## ci.ub¹
## intrcpt -0.1378 ***
## log(timepoint_mean) 0.0715 ***
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## 1) results based on cluster-robust inference (var-cov estimator: CR2,
## approx t/F-tests and confidence intervals, df: Satterthwaite approx)## Profiling tau2 = 1
## Profiling rho = 1
| 1 year | 2 years | 5 years | Zero crossing | Last Data Point |
|---|---|---|---|---|
| 93.5 (92 to 95.1) | 96.9 (94.9 to 98.9) | 101.5 (98 to 105.2) | 28 months | 94 months |
## [1] 26.332883. Triple Crossover Hop
Specify covariance matrix
Model Selection
## [[1]]
## mod logLik. deviance. AIC. BIC. AICc.
## 1 Linear 39.85827 -79.71653 -71.71653 -65.27286 -70.46653
## 2 Log 42.70753 -85.41506 -77.41506 -70.97139 -76.16506
## 3 Poly (2) 40.39153 -80.78305 -70.78305 -62.86546 -68.78305
## 4 3 knot RCS 42.03468 -84.06936 -74.06936 -66.15177 -72.06936
## 5 4 knot RCS 41.24803 -82.49607 -70.49607 -61.16398 -67.49607
##
## [[2]]
Final Model - Triple Crossover Hop
##
## Multivariate Meta-Analysis Model (k = 39; method: REML)
##
## Variance Components:
##
## outer factor: cohort (nlvls = 29)
## inner factor: timepoint_mean (nlvls = 29)
##
## estim sqrt fixed
## tau^2 0.0075 0.0864 no
## rho 0.9736 no
##
## Test for Residual Heterogeneity:
## QE(df = 37) = 1247.9040, p-val < .0001
##
## Number of estimates: 39
## Number of clusters: 29
## Estimates per cluster: 1-3 (mean: 1.34, median: 1)
##
## Test of Moderators (coefficient 2):¹
## F(df1 = 1, df2 = 11.29) = 13.3637, p-val = 0.0036
##
## Model Results:
##
## estimate se¹ tval¹ df¹ pval¹ ci.lb¹
## intrcpt -0.2404 0.0535 -4.4973 17.01 0.0003 -0.3532
## log(timepoint_mean) 0.0617 0.0169 3.6556 11.29 0.0036 0.0247
## ci.ub¹
## intrcpt -0.1276 ***
## log(timepoint_mean) 0.0988 **
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## 1) results based on cluster-robust inference (var-cov estimator: CR2,
## approx t/F-tests and confidence intervals, df: Satterthwaite approx)## Profiling tau2 = 1
## Profiling rho = 1
| 1 year | 2 years | 5 years | Zero crossing | Last Data Point |
|---|---|---|---|---|
| 91.7 (88.7 to 94.7) | 95.7 (93.1 to 98.4) | 101.2 (96.4 to 106.3) | 30 months | 94 months |
## [1] 16.041134. Side Hop
Specify covariance matrix
Model Selection
## [[1]]
## mod logLik. deviance. AIC. BIC. AICc.
## 1 Linear 19.46570 -38.93140 -30.93140 -27.59855 -27.59807
## 2 Log 20.50714 -41.01428 -33.01428 -29.68143 -29.68095
## 3 Poly (2) 19.36695 -38.73390 -28.73390 -24.87095 -22.73390
## 4 3 knot RCS 22.73347 -45.46693 -35.46693 -31.60399 -29.46693
## 5 4 knot RCS 22.51515 -45.03030 -33.03030 -28.78200 -22.53030
##
## [[2]]
Final Model - Side Hop
##
## Multivariate Meta-Analysis Model (k = 19; method: REML)
##
## Variance Components:
##
## outer factor: cohort (nlvls = 13)
## inner factor: timepoint_mean (nlvls = 15)
##
## estim sqrt fixed
## tau^2 0.0057 0.0758 no
## rho 0.9981 no
##
## Test for Residual Heterogeneity:
## QE(df = 16) = 264.3766, p-val < .0001
##
## Number of estimates: 19
## Number of clusters: 13
## Estimates per cluster: 1-3 (mean: 1.46, median: 1)
##
## Test of Moderators (coefficients 2:3):¹
## F(df1 = 2, df2 = 1.5) = 121.3381, p-val = 0.0219
##
## Model Results:
##
## estimate se¹ tval¹ df¹
## intrcpt -0.3477 0.0233 -14.9472 5.86
## rcs(timepoint_mean, 3)timepoint_mean 0.0248 0.0018 13.7188 2.16
## rcs(timepoint_mean, 3)timepoint_mean' -0.0200 0.0020 -9.9507 2.85
## pval¹ ci.lb¹ ci.ub¹
## intrcpt <.0001 -0.4050 -0.2905 ***
## rcs(timepoint_mean, 3)timepoint_mean 0.0039 0.0175 0.0321 **
## rcs(timepoint_mean, 3)timepoint_mean' 0.0027 -0.0266 -0.0134 **
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## 1) results based on cluster-robust inference (var-cov estimator: CR2,
## approx t/F-tests and confidence intervals, df: Satterthwaite approx)## Profiling tau2 = 1
## Profiling rho = 1
| 1 year | 2 years | 5 years | Zero crossing | Last Data Point |
|---|---|---|---|---|
| 92.8 (87.9 to 98) | 95.8 (91.3 to 100.5) | 99 (88.1 to 111.3) | 15 months | 62 months |
## [1] -3.899879## [1] 6.50000 11.08165 18.000005. Vertical Hop
Specify covariance matrix
Model Selection
## [[1]]
## mod logLik. deviance. AIC. BIC. AICc.
## 1 Linear 35.14039 -70.28077 -62.28077 -57.24839 -60.37601
## 2 Log 37.21730 -74.43461 -66.43461 -61.40222 -64.52985
## 3 Poly (2) 35.00802 -70.01605 -60.01605 -53.92167 -56.85815
## 4 3 knot RCS 36.97917 -73.95833 -63.95833 -57.86395 -60.80044
## 5 4 knot RCS 35.15689 -70.31378 -58.31378 -51.24546 -53.37261
##
## [[2]]
Final Model - Vertical Hop
##
## Multivariate Meta-Analysis Model (k = 28; method: REML)
##
## Variance Components:
##
## outer factor: cohort (nlvls = 22)
## inner factor: timepoint_mean (nlvls = 20)
##
## estim sqrt fixed
## tau^2 0.0029 0.0541 no
## rho 0.6086 no
##
## Test for Residual Heterogeneity:
## QE(df = 26) = 538.2331, p-val < .0001
##
## Number of estimates: 28
## Number of clusters: 22
## Estimates per cluster: 1-3 (mean: 1.27, median: 1)
##
## Test of Moderators (coefficient 2):¹
## F(df1 = 1, df2 = 9.53) = 11.1711, p-val = 0.0080
##
## Model Results:
##
## estimate se¹ tval¹ df¹ pval¹ ci.lb¹
## intrcpt -0.2864 0.0496 -5.7796 12.96 <.0001 -0.3935
## log(timepoint_mean) 0.0594 0.0178 3.3423 9.53 0.0080 0.0195
## ci.ub¹
## intrcpt -0.1793 ***
## log(timepoint_mean) 0.0992 **
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## 1) results based on cluster-robust inference (var-cov estimator: CR2,
## approx t/F-tests and confidence intervals, df: Satterthwaite approx)## Profiling tau2 = 1
## Profiling rho = 1
| 1 year | 2 years | 5 years | Zero crossing | Last Data Point |
|---|---|---|---|---|
| 87 (85.3 to 88.8) | 90.7 (88.4 to 93.1) | 95.8 (90.2 to 101.7) | 51 months | 55 months |
## [1] 34.016456. 6m timed Hop
Specify covariance matrix
Model Selection
## [[1]]
## mod logLik. deviance. AIC. BIC. AICc.
## 1 Linear 45.28073 -90.56147 -82.56147 -76.22739 -81.27115
## 2 Log 49.05946 -98.11892 -90.11892 -83.78484 -88.82860
## 3 Poly (2) 45.91722 -91.83444 -81.83444 -74.05770 -79.76547
## 4 3 knot RCS 47.91608 -95.83217 -85.83217 -78.05543 -83.76320
## 5 4 knot RCS 47.00637 -94.01275 -82.01275 -72.85458 -78.90164
##
## [[2]]
Final Model - 6m timed hop
##
## Multivariate Meta-Analysis Model (k = 38; method: REML)
##
## Variance Components:
##
## outer factor: cohort (nlvls = 25)
## inner factor: timepoint_mean (nlvls = 29)
##
## estim sqrt fixed
## tau^2 0.0034 0.0584 no
## rho 0.0529 no
##
## Test for Residual Heterogeneity:
## QE(df = 36) = 810.6433, p-val < .0001
##
## Number of estimates: 38
## Number of clusters: 25
## Estimates per cluster: 1-4 (mean: 1.52, median: 1)
##
## Test of Moderators (coefficient 2):¹
## F(df1 = 1, df2 = 7.45) = 19.0457, p-val = 0.0028
##
## Model Results:
##
## estimate se¹ tval¹ df¹ pval¹ ci.lb¹
## intrcpt -0.2170 0.0365 -5.9410 9.41 0.0002 -0.2991
## log(timepoint_mean) 0.0566 0.0130 4.3641 7.45 0.0028 0.0263
## ci.ub¹
## intrcpt -0.1349 ***
## log(timepoint_mean) 0.0870 **
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## 1) results based on cluster-robust inference (var-cov estimator: CR2,
## approx t/F-tests and confidence intervals, df: Satterthwaite approx)## Profiling tau2 = 1
## Profiling rho = 1
| 1 year | 2 years | 5 years | Zero crossing | Last Data Point |
|---|---|---|---|---|
| 92.7 (90.6 to 94.8) | 96.4 (93.7 to 99.1) | 101.5 (96.5 to 106.8) | 27 months | 94 months |
## [1] 36.02217Case Control
Significantly less data available for between person/case control comparisons. Only single hop has enough data to run same analysis as within person.
1. Single Hop - Between Person
Specify covariance matrix
Model Selection
## [[1]]
## mod logLik. deviance. AIC. BIC. AICc.
## 1 Linear 15.42067 -30.84133 -22.84133 -19.75098 -19.204971
## 2 Log 16.82728 -33.65455 -25.65455 -22.56420 -22.018191
## 3 Poly (2) 15.23835 -30.47671 -20.47671 -16.93645 -13.810039
## 4 3 knot RCS 17.66685 -35.33370 -25.33370 -21.79345 -18.667032
## 5 4 knot RCS 15.82739 -31.65477 -19.65477 -15.82043 -7.654771
##
## [[2]]
Final Model - Single Leg Hop
##
## Multivariate Meta-Analysis Model (k = 18; method: REML)
##
## Variance Components:
##
## outer factor: cohort (nlvls = 15)
## inner factor: timepoint_mean (nlvls = 17)
##
## estim sqrt fixed
## tau^2 0.0070 0.0835 no
## rho 1.0000 no
##
## Test for Residual Heterogeneity:
## QE(df = 16) = 127.1249, p-val < .0001
##
## Number of estimates: 18
## Number of clusters: 15
## Estimates per cluster: 1-3 (mean: 1.20, median: 1)
##
## Test of Moderators (coefficient 2):¹
## F(df1 = 1, df2 = 2.67) = 5.5065, p-val = 0.1114
##
## Model Results:
##
## estimate se¹ tval¹ df¹ pval¹ ci.lb¹
## intrcpt -0.2924 0.0722 -4.0512 3.59 0.0192 -0.5021
## log(timepoint_mean) 0.0606 0.0258 2.3466 2.67 0.1114 -0.0276
## ci.ub¹
## intrcpt -0.0827 *
## log(timepoint_mean) 0.1488
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## 1) results based on cluster-robust inference (var-cov estimator: CR2,
## approx t/F-tests and confidence intervals, df: Satterthwaite approx)## Profiling tau2 = 1
## Profiling rho = 1
| 1 year | 2 years | 5 years | Zero crossing | Last Data Point |
|---|---|---|---|---|
| 86.8 (82.4 to 91.4) | 90.5 (85.1 to 96.3) | 95.7 (84.9 to 107.8) | 34 months | 62 months |
## [1] 7.7250322. Triple Hop / Triple Crossover Hop - Between Person
Not enough data to be able to run longitudinal analysis. Reverting to univariate meta analysis.
## ROM 95%-CI %W(common) %W(random)
## Casp 2021 0.8750 [0.8287; 0.9239] 33.5 33.5
## Gokeler 2017a 0.8784 [0.8353; 0.9237] 39.0 39.0
## Kline 2018 0.8035 [0.7088; 0.9108] 6.3 6.3
## Norte 2020 0.8985 [0.8392; 0.9619] 21.2 21.2
##
## Number of studies: k = 4
##
## ROM 95%-CI z p-value
## Common effect model 0.8765 [0.8494; 0.9045] -8.22 < 0.0001
## Random effects model 0.8765 [0.8494; 0.9045] -8.21 < 0.0001
##
## Quantifying heterogeneity:
## tau^2 < 0.0001 [0.0000; 0.0303]; tau = 0.0007 [0.0000; 0.1741]
## I^2 = 0.0% [0.0%; 84.7%]; H = 1.00 [1.00; 2.56]
##
## Test of heterogeneity:
## Q d.f. p-value
## 2.37 3 0.4995
##
## Details on meta-analytical method:
## - Inverse variance method
## - Restricted maximum-likelihood estimator for tau^2
## - Q-Profile method for confidence interval of tau^2 and tau
## ROM 95%-CI %W(common) %W(random)
## Patterson 2020a 0.8349 [0.7469; 0.9333] 27.3 27.5
## Kline 2018 0.8161 [0.7011; 0.9501] 14.7 14.9
## Norte 2020 0.8934 [0.8276; 0.9645] 58.0 57.6
##
## Number of studies: k = 3
##
## ROM 95%-CI z p-value
## Common effect model 0.8654 [0.8165; 0.9174] -4.86 < 0.0001
## Random effects model 0.8652 [0.8157; 0.9176] -4.82 < 0.0001
##
## Quantifying heterogeneity:
## tau^2 < 0.0001 [0.0000; 0.0845]; tau = 0.0064 [0.0000; 0.2907]
## I^2 = 0.0% [0.0%; 89.6%]; H = 1.00 [1.00; 3.10]
##
## Test of heterogeneity:
## Q d.f. p-value
## 1.64 2 0.4412
##
## Details on meta-analytical method:
## - Inverse variance method
## - Restricted maximum-likelihood estimator for tau^2
## - Q-Profile method for confidence interval of tau^2 and tau
3. Side Hop - Between Person
Not enough data to be able to run longitudinal analysis. Reverting to univariate meta analysis.
- Only 4 studies, 1 with multiple timepoint (Patterson)
- 3 <24m, 2 > 50m.
## ROM 95%-CI %W(common) %W(random)
## Patterson 2020a 0.7080 [0.5807; 0.8632] 12.3 18.4
## Engelen-VanMelick 2017 0.8067 [0.6709; 0.9700] 14.3 20.1
## Falstrom 2017 0.9282 [0.8161; 1.0557] 29.3 28.5
## Faltstrom 2021 0.9032 [0.8133; 1.0030] 44.1 33.0
##
## Number of studies: k = 4
##
## ROM 95%-CI z p-value
## Common effect model 0.8694 [0.8109; 0.9321] -3.94 < 0.0001
## Random effects model 0.8508 [0.7631; 0.9486] -2.91 0.0036
##
## Quantifying heterogeneity:
## tau^2 = 0.0065 [0.0000; 0.2044]; tau = 0.0805 [0.0000; 0.4521]
## I^2 = 52.1% [0.0%; 84.2%]; H = 1.44 [1.00; 2.51]
##
## Test of heterogeneity:
## Q d.f. p-value
## 6.26 3 0.0997
##
## Details on meta-analytical method:
## - Inverse variance method
## - Restricted maximum-likelihood estimator for tau^2
## - Q-Profile method for confidence interval of tau^2 and tau
4. Vertical Hop - Between Person
Not enough data to be able to run longitudinal analysis. Reverting to univariate meta analysis.
- Only 5 studies, varied timepoints
## ROM 95%-CI %W(common) %W(random)
## Engelen-VanMelick 2017 0.9492 [0.8467; 1.0641] 17.0 23.5
## Laudner 2015 0.8718 [0.7796; 0.9748] 17.8 23.8
## Markstrom 2023 1.0000 [0.9263; 1.0796] 37.8 26.9
## O'Malley 2018 0.7706 [0.7042; 0.8432] 27.4 25.8
##
## Number of studies: k = 4
##
## ROM 95%-CI z p-value
## Common effect model 0.9007 [0.8592; 0.9442] -4.35 < 0.0001
## Random effects model 0.8940 [0.7963; 1.0037] -1.90 0.0577
##
## Quantifying heterogeneity:
## tau^2 = 0.0114 [0.0022; 0.1779]; tau = 0.1068 [0.0466; 0.4218]
## I^2 = 84.9% [62.3%; 93.9%]; H = 2.57 [1.63; 4.05]
##
## Test of heterogeneity:
## Q d.f. p-value
## 19.82 3 0.0002
##
## Details on meta-analytical method:
## - Inverse variance method
## - Restricted maximum-likelihood estimator for tau^2
## - Q-Profile method for confidence interval of tau^2 and tau
5. 6m timed Hop - Between Person
Not enough data to be able to run longitudinal analysis. Reverting to univariate meta analysis.
- Only 2 studies
## ROM 95%-CI %W(common) %W(random)
## Kline 2018 0.6970 [0.5287; 0.9188] 13.0 30.3
## Norte 2020 0.8571 [0.7701; 0.9540] 87.0 69.7
##
## Number of studies: k = 2
##
## ROM 95%-CI z p-value
## Common effect model 0.8343 [0.7551; 0.9219] -3.56 0.0004
## Random effects model 0.8051 [0.6683; 0.9700] -2.28 0.0226
##
## Quantifying heterogeneity:
## tau^2 = 0.0100; tau = 0.0998; I^2 = 46.6%; H = 1.37
##
## Test of heterogeneity:
## Q d.f. p-value
## 1.87 1 0.1713
##
## Details on meta-analytical method:
## - Inverse variance method
## - Restricted maximum-likelihood estimator for tau^2
Regression of True Effects
Using studies which measure 2 hop tests concurrently, we run a bivariate analysis.
We have to account for non-independence of samples in the analysis conducting a variance/covariance matrix and also fitting random effects for this (type of outcome: within/between person nested within cohorts). To calculate this we assumed a rho for each hop test.
Single hop and other forward hops - 0.7 Single hop and side hop/vertical hop - 0.7
Sensitivity analyses show that estimates are stable to different values for this.
Single hop and Triple hop
##
## Multivariate Meta-Analysis Model (k = 62; method: REML)
##
## Variance Components:
##
## outer factor: cohort (nlvls = 31)
## inner factor: measure (nlvls = 2)
##
## estim sqrt k.lvl fixed level
## tau^2.1 0.0014 0.0374 31 no triple hop
## tau^2.2 0.0016 0.0404 31 no single hop
##
## rho.trph rho.sngh trph sngh
## triple hop 1 - 31
## single hop 0.9608 1 no -
##
## Test for Residual Heterogeneity:
## QE(df = 60) = 797.9911, p-val < .0001
##
## Test of Moderators (coefficients 1:2):
## QM(df = 2) = 119.3674, p-val < .0001
##
## Model Results:
##
## estimate se zval pval ci.lb ci.ub
## measuretriple hop -0.0732 0.0070 -10.3966 <.0001 -0.0870 -0.0594 ***
## measuresingle hop -0.0833 0.0076 -10.9208 <.0001 -0.0982 -0.0683 ***
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## [[1]]
##
## estimate se zval pval ci.lb ci.ub
## intrcpt -0.0469 0.0713 -0.6576 0.5108 -0.1865 0.0928
## triple hop 1.0404 0.0767 13.5705 <.0001 0.8901 1.1906 ***
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## [[2]]
Single hop and Vertical hop
##
## Multivariate Meta-Analysis Model (k = 22; method: REML)
##
## Variance Components:
##
## outer factor: cohort (nlvls = 10)
## inner factor: measure (nlvls = 2)
##
## estim sqrt k.lvl fixed level
## tau^2.1 0.0014 0.0381 11 no vertical hop
## tau^2.2 0.0004 0.0203 11 no single hop
##
## rho.vrth rho.sngh vrth sngh
## vertical hop 1 - 10
## single hop 0.2696 1 no -
##
## Test for Residual Heterogeneity:
## QE(df = 20) = 187.8013, p-val < .0001
##
## Test of Moderators (coefficients 1:2):
## QM(df = 2) = 118.6979, p-val < .0001
##
## Model Results:
##
## estimate se zval pval ci.lb ci.ub
## measurevertical hop -0.1172 0.0130 -9.0397 <.0001 -0.1426 -0.0918 ***
## measuresingle hop -0.0626 0.0072 -8.6427 <.0001 -0.0768 -0.0484 ***
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## [[1]]
##
## estimate se zval pval ci.lb ci.ub
## intrcpt 0.8118 0.1897 4.2798 <.0001 0.4400 1.1836 ***
## vertical hop 0.1434 0.2133 0.6724 0.5013 -0.2746 0.5614
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## [[2]]
Single hop and Side hop
##
## Multivariate Meta-Analysis Model (k = 26; method: REML)
##
## Variance Components:
##
## outer factor: cohort (nlvls = 12)
## inner factor: measure (nlvls = 2)
##
## estim sqrt k.lvl fixed level
## tau^2.1 0.0033 0.0570 13 no side hop
## tau^2.2 0.0015 0.0386 13 no single hop
##
## rho.sdhp rho.sngh sdhp sngh
## side hop 1 - 12
## single hop 0.8195 1 no -
##
## Test for Residual Heterogeneity:
## QE(df = 24) = 367.6610, p-val < .0001
##
## Test of Moderators (coefficients 1:2):
## QM(df = 2) = 27.3344, p-val < .0001
##
## Model Results:
##
## estimate se zval pval ci.lb ci.ub
## measureside hop -0.0893 0.0175 -5.1129 <.0001 -0.1235 -0.0551 ***
## measuresingle hop -0.0553 0.0117 -4.7347 <.0001 -0.0782 -0.0324 ***
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## [[1]]
##
## estimate se zval pval ci.lb ci.ub
## intrcpt 0.4395 0.1282 3.4281 0.0006 0.1882 0.6908 ***
## side hop 0.5540 0.1402 3.9518 <.0001 0.2792 0.8288 ***
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## [[2]]
Single hop and 6 timed hop
##
## Multivariate Meta-Analysis Model (k = 38; method: REML)
##
## Variance Components:
##
## outer factor: cohort (nlvls = 19)
## inner factor: measure (nlvls = 2)
##
## estim sqrt k.lvl fixed level
## tau^2.1 0.0020 0.0442 19 no 6m timed hop
## tau^2.2 0.0013 0.0364 19 no single hop
##
## rho.6mth rho.sngh 6mth sngh
## 6m timed hop 1 - 19
## single hop 0.8733 1 no -
##
## Test for Residual Heterogeneity:
## QE(df = 36) = 438.3183, p-val < .0001
##
## Test of Moderators (coefficients 1:2):
## QM(df = 2) = 86.5826, p-val < .0001
##
## Model Results:
##
## estimate se zval pval ci.lb ci.ub
## measure6m timed hop -0.0732 0.0108 -6.7845 <.0001 -0.0944 -0.0521 ***
## measuresingle hop -0.0811 0.0089 -9.1511 <.0001 -0.0985 -0.0637 ***
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## [[1]]
##
## estimate se zval pval ci.lb ci.ub
## intrcpt 0.2548 0.1252 2.0347 0.0419 0.0094 0.5002 *
## 6m timed hop 0.7180 0.1347 5.3289 <.0001 0.4539 0.9821 ***
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## [[2]]
Triple hop and Triple crossover hop
##
## Multivariate Meta-Analysis Model (k = 40; method: REML)
##
## Variance Components:
##
## outer factor: cohort (nlvls = 20)
## inner factor: measure (nlvls = 2)
##
## estim sqrt k.lvl fixed level
## tau^2.1 0.0020 0.0445 20 no triple crossover hop
## tau^2.2 0.0019 0.0441 20 no triple hop
##
## rho.trch rho.trph trch trph
## triple crossover hop 1 - 20
## triple hop 0.9819 1 no -
##
## Test for Residual Heterogeneity:
## QE(df = 38) = 842.6705, p-val < .0001
##
## Test of Moderators (coefficients 1:2):
## QM(df = 2) = 61.3503, p-val < .0001
##
## Model Results:
##
## estimate se zval pval ci.lb
## measuretriple crossover hop -0.0779 0.0104 -7.4925 <.0001 -0.0983
## measuretriple hop -0.0802 0.0103 -7.8198 <.0001 -0.1003
## ci.ub
## measuretriple crossover hop -0.0575 ***
## measuretriple hop -0.0601 ***
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## [[1]]
##
## estimate se zval pval ci.lb ci.ub
## intrcpt 0.0217 0.0564 0.3858 0.6996 -0.0887 0.1322
## triple crossover hop 0.9742 0.0609 15.9881 <.0001 0.8548 1.0937 ***
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## [[2]]
Triple crossover and 6m
##
## Multivariate Meta-Analysis Model (k = 32; method: REML)
##
## Variance Components:
##
## outer factor: cohort (nlvls = 16)
## inner factor: measure (nlvls = 2)
##
## estim sqrt k.lvl fixed level
## tau^2.1 0.0027 0.0516 16 no 6m timed hop
## tau^2.2 0.0016 0.0403 16 no triple crossover hop
##
## rho.6mth rho.trch 6mth trch
## 6m timed hop 1 - 16
## triple crossover hop 0.7293 1 no -
##
## Test for Residual Heterogeneity:
## QE(df = 30) = 727.9863, p-val < .0001
##
## Test of Moderators (coefficients 1:2):
## QM(df = 2) = 49.2613, p-val < .0001
##
## Model Results:
##
## estimate se zval pval ci.lb
## measure6m timed hop -0.0754 0.0137 -5.5179 <.0001 -0.1022
## measuretriple crossover hop -0.0747 0.0107 -6.9924 <.0001 -0.0956
## ci.ub
## measure6m timed hop -0.0486 ***
## measuretriple crossover hop -0.0537 ***
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## [[1]]
##
## estimate se zval pval ci.lb ci.ub
## intrcpt 0.3999 0.1453 2.7526 0.0059 0.1152 0.6847 **
## 6m timed hop 0.5695 0.1567 3.6350 0.0003 0.2624 0.8766 ***
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## [[2]]
Triple hop and 6m
##
## Multivariate Meta-Analysis Model (k = 32; method: REML)
##
## Variance Components:
##
## outer factor: cohort (nlvls = 16)
## inner factor: measure (nlvls = 2)
##
## estim sqrt k.lvl fixed level
## tau^2.1 0.0026 0.0505 16 no 6m timed hop
## tau^2.2 0.0013 0.0365 16 no triple hop
##
## rho.6mth rho.trph 6mth trph
## 6m timed hop 1 - 16
## triple hop 0.8079 1 no -
##
## Test for Residual Heterogeneity:
## QE(df = 30) = 548.8912, p-val < .0001
##
## Test of Moderators (coefficients 1:2):
## QM(df = 2) = 58.4267, p-val < .0001
##
## Model Results:
##
## estimate se zval pval ci.lb ci.ub
## measure6m timed hop -0.0763 0.0133 -5.7132 <.0001 -0.1024 -0.0501 ***
## measuretriple hop -0.0728 0.0096 -7.6154 <.0001 -0.0916 -0.0541 ***
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## [[1]]
##
## estimate se zval pval ci.lb ci.ub
## intrcpt 0.3891 0.1207 3.2244 0.0013 0.1526 0.6257 **
## 6m timed hop 0.5835 0.1302 4.4798 <.0001 0.3282 0.8387 ***
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## [[2]]